线性矩阵方程的迭代求解方法  

On the iterative method of linear matrix equation

作　　者：蔺小林[1] 霍佩佩[1] 

机构地区：[1]陕西科技大学理学院,陕西西安710021

出　　处：《陕西科技大学学报（自然科学版）》2015年第1期175-178,183,共5页Journal of Shaanxi University of Science & Technology

基　　金：陕西省科技厅重点实验室科研计划项目(2011HBSZS014);陕西科技大学学术团队计划项目(2013XSD39)

摘　　要：在很多问题中会遇到线性矩阵方程的求解问题,如果线性矩阵方程用矩阵直积和矩阵按行或按列进行拉直,用向量表示未知数不仅不方便,而且占用空间较大,因此有必要讨论线性矩阵方程的数值求解方法.本文给出了线性矩阵方程的迭代求解方法,讨论了迭代方法收敛的条件,给出了线性矩阵方程的雅可比迭代方法和方阵乘幂求和方法,用数值例子基于Matlab程序验证了算法的可行性.We often encounter the problem of solving linear matrix equations in a number of situations such as Kronecker product and transform a matrix by line or by column into a vector.It is inconvenient to represent unknown variables with a vector and it will occupy a large space inevitable.Therefore,it is very necessary to search the solution of linear matrix equations.In this paper,we formulate an iterative procedure to solve linear matrix equations,discuss the convergence condition of our iterative procedure and present the Jacobi method and the summation of square matrix′s power of linear matrix equations.Numerical experiments based on Matlab show the effectiveness of the proposed algorithm.

关 键 词：线性矩阵方程 雅可比迭代法 收敛性 方阵乘幂求和法 

分 类 号：O151.21[理学—数学]